一类中立型高维周期微分系统的周期解

Periodic Solutions To a Class of Neutral Higher Dimensional Periodic Differential System

本文考虑中立型高维周期系统：其中（L，x）∈R×R^n，A（t，x）为连续函数矩阵，x_t∈C（[-γ,0]，R^n），x_t（θ）＝x（t十θ），θ∈[-r,0]，记C＝C（[-r,0］，R^n），f：R×C→R^n连续，且A（t＋T，X）＝A（t，x），T,r＞c∈R，本文用不动点方法研究此系统，得到了其周期解存在的充分性条件，所得结果推广、改进了文［1－3］中相应结论．

In this paper, we cosider the neutral higher dimensional periodic system:Where (t, x) ∈ R ×Rn, the n×n matrix A(t, x) is continuous, xt ∈C([-r, 0], Rn),xt(9) = x(t + θ), 0 E [-r, 0], denote C = C([-r, 0], Rn), f. R ×C→ Rn is continuous,furthermore A(t + T, x) = A(t, x)∈(t,x) E R ×Rn, f(t + T, ) = f(t,),(t，) ER × C, T, r ＞ 0, c ∈R. Using fixed point method, we get some sufficient conditionsto guarantee the existence and uniqueness of T-periodic solutions for the system. Thecorresponding results in [1-3] are extended and improved.